Labeled Trees Generating Separable and Locally Finite Ultrametrics

2025/06/04 by Dovgoshey, Oleksiy, Rovenska, Olga · 4 citations
#05C05 #05C63 #54E35 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2506.03853

Abstract

We analyze the interplay between labeled trees and the ultrametric spaces they present. We provide characterizations of labeled trees that generate separable ultrametric spaces and those that generate locally finite ultrametric spaces. In particular, we establish an analog of König's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees.

Cited by

• Longest paths in trees and isometricity of ultrametric spaces
• Forbidden Four Cycle, Star Graphs and Isometric Embeddings
• On convergence structures in infinite graphs
• Hausdorff distance between ultrametric balls

Related

• Konig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees
• Labeled trees generating complete, compact, and discrete ultrametric spaces
• Locally finite ultrametric spaces and labeled trees
• Extremal properties and morphisms of finite ultrametric spaces and their representing trees
• Totally bounded ultrametric spaces and locally finite trees